Global existence and asymptotic stability near equilibrium for the relativistic BGK model. (February 2015)

• Record Type: Journal Article
• Authors: Bellouquid, A.; Nieto, J.; Urrutia, L.
• Is Part Of: Nonlinear analysis. Volume 114(2015)
• Page Start: 87
• Page End: 104
• Publication Date: 2015-02
• Subjects: BGK -- Boltzmann -- Relativistic equations -- Kinetic theory -- Equilibrium decay -- Jüttner function; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.10.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, the relativistic BGK model is studied. The Jüttner function is presented as the relativistic counterpart of the local Maxwellian equilibrium in the classical case. By linearization around this equilibrium, we obtain a linearized relativistic BGK model and study their time decay at infinity. Finally, existence and asymptotic behavior of close-to-equilibrium solutions of the whole nonlinear relativistic BGK model are proved.